Function Optimization with Latent Variable Models

Most of estimation of distribution algorithms (EDAs) try to represent explicitly the relationship between variables with factorization tech- niques or with graphical models such as Bayesian networks. In this paper, we propose to use latent variable models such as Helmholtz machine and probabilistic principal component analysis for capturing the probabilistic distribution of given data. The latent variable models are statistical models that specify the relationships between a set of random variables and a set of latent variables; Latent variables are not directly observable and there are a smaller number of variables in latent variables than in input variables. In statistics latent variable models are used for density estimation. Since latent variable models are generative models, it is easy to sample a new data. Our experimental results support that the proposed latent variable models can find good solutions more efficiently than other EDAs for continuous functions.